Some characterizations for the exponential \(\varphi\)-expansiveness of linear skew-product semiflows. (Chinese. English summary) Zbl 1499.37021
Summary: The exponential \(\varphi\)-expansiveness of linear skew-product semiflows in Banach space was studied. Based on the definition of uniform exponential expansiveness, a linear skew-product semiflow with exponential \(\varphi\)-expansiveness was presented. Some characterizations for exponential \(\varphi\)-expansiveness were obtained via mathematical analysis and operator theory. The results extend some well-known conclusions in the exponential stability theory.
MSC:
37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
37C10 | Dynamics induced by flows and semiflows |
37C75 | Stability theory for smooth dynamical systems |